Researchers for a company that manufactures batteries want to test the hypothesis that the mean battery life of their new battery is greater than the known mean battery life of their older version. The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample. Which of the following is an appropriate test for the researchers' hypothesis?

a. A one-sample z-test for a population mean.
b. A one-sample t-test for a population mean.
c. A one-sample z-test for a population proportion.
d. A matched-pairs t-test for a mean difference
e. A two-sample t-test for a difference between means

On solving the provided question, we can say that - he re the slope value is using the formula y/x = k => [tex]k = 2/3[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

Use the point (3, 2) and divide y by x using the formula y/x = k.

[tex]k = 2/3[/tex]

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Answer: To reflect a point across the x-axis, you need to change the sign of the y-coordinate. Therefore, the point (-7.2, 2) reflected across the x-axis becomes (-7.2, -2).

To reflect a point across the y-axis, you need to change the sign of the x-coordinate. Therefore, the point (-7.2, -2) reflected across the y-axis becomes (7.2, -2).

The resulting shape is a rectangle with one corner at (-7.2, 2) and the opposite corner at (7.2, -2).

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. JK ∥ LM, KL ∥ MN                                 Given

2. ∠KJL ≅ ∠MLN; ∠KLJ ≅ ∠MNL           c. Corresponding Angles  

3. JK ≅ LM                                               Given

4. ∆JKL ≅ ∆LMN                                     e. AAS

The product of the given numbers can be represented in a scientific notation form as = 6418 × 10^19 (approximately)

Multiplication can be defined as the repeated addition of a given value with the purpose of arriving to an expected value.

The multiplication of two given numbers is the same thing as the products of the given number and it's represented by the sign (X)

The product of 6,789,694,976 x 9,452,569,132 = 6418 × 10^19

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The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.

A system of linear equations consists of two or more equations and looks for common answers.

1. Let us suppose small prints = x

Large prints = y

Total prints sold can be written as follows:

x + y = 52

The total cost of the prints can be written as follows:

50x + 75y = 2975

The system of equations is:

x + y = 52   . . . equation 1

50x + 75y = 2975 . . .equation 2

Using equation 1 we have:

x = 52 - y

Substituting the value of x in equation 2 we have:

50(52 - y) + 75y = 2975

2600 - 50y + 75y = 2975

25y = 2975 - 2600

25y = 375

y = 15

Now, substituting the value of y in equation 1 we have:

x + 15 = 52

x = 52 - 15

x = 37

Hence, the solution of the system of equations is y = 15 and x = 37.

2. Let us suppose the altitude = x.

The rising balloon can be thus written as:

40 +10x

The descending balloon can be written as:

165 - 15x

Solving the system of equations by substituting the value of x we get x= 5.

Hence, the altitude at which both the balloons are at the same height is 5m.

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the answer is right there

Answer:

m<1=90°

m<2=38°

hope this helps

Answer:

48

Step-by-step explanation:

The component vectors to a linear combination is given by the equation

A = 20 i^ + 14 j^ - 23 k^

The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by

u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃

An equivalent definition, typically used in physics, is

u ⋅ v = ∣u∣ ∣v∣ cos θ,

where θ is the angle between u and v

Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero

Given data ,

Let the component vectors be represented as A

The value of A is

< 20 , 14 , -23 >   be equation (1)

On simplifying the equation to the linear combination , we get

< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^

So , the linear combination of the vectors is given by the equation ,

A = 20 i^ + 14 j^ - 23 k^

Hence , the equation is 20 i^ + 14 j^ - 23 k^

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Answer:

195°

Step-by-step explanation:

Answer:

n=15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

First off we divide both sides by [tex]\frac{1}{5}[/tex] and get:

[tex]\frac{1}{5}[/tex]n÷ [tex]\frac{1}{5}[/tex]=3÷ [tex]\frac{1}{5}[/tex]

n=3×5

n=15

Answer:

Number of students in district = 3,055 students

Step-by-step explanation:

Given:

Ratio [Teachers to students] = 2 : 47

Total number of teachers in district = 130

Find:

Number of students in district

Computation:

Number of students in district = Total number of teachers in district[47/2]

Number of students in district = 130[47/2]

Number of students in district = 65[47]

Number of students in district = 3,055 students

Answer:

28 units

Step-by-step explanation:

ABCD is a rectangle. AC and BD are diagonals intersecting at point E.

Diagonals of a rectangle bisect each other.

[tex] \therefore BE = ED[/tex]

[tex] \therefore 6x + 2 = 4x + 6[/tex]

[tex] \therefore 6x - 4x= 6-2[/tex]

[tex] \therefore 2x= 4[/tex]

[tex] \therefore x= \frac{4}{2} [/tex]

[tex] \therefore x= 2 [/tex]

[tex] \therefore 6x + 2= 6*2+2= 12+2= 14 [/tex]

[tex] \therefore BE= 14\: units [/tex]

[tex] \because BD = 2BE[/tex]

[tex] \therefore BD = 2(14)= 28\: units [/tex]

[tex] \because AC = BD[/tex] (diagonals of a are equal in measure)

[tex] \therefore AC = 28\: units [/tex]

Answer:

Make sure you include the words ^-^

Step-by-step explanation:

Answer:

Step-by-step explanation:

you add all them up

Answer:

C.

Step-by-step explanation:

there is a measuement of 12 cm missing.

Just multiply all the sides!

The current temperature of the water is given as follows:

71.7 ºF.

The defining statement from the problem is given as follows:

He finds that the temperature changed by -0.6°F.

The change by the negative amount of -0.6ºF means that the current temperature of the water is obtained subtracting the previous temperature of the water by 0.6 ºF.

The previous temperature of the water is given as follows:

72.3°F.

Hence the current temperature of the water is obtained subtracting 72.3ºF and 0.6ºF, as follows:

72.3 - 0.6 = 71.7 ºF.

The previous temperature of the water is given as follows:

72.3°F.

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Answer:

6 is the missing number

Step-by-step explanation:

Solve what is inside of the parenthesis, then evaluate.

N x (8) = (30) + (18)

8N = 48

Solve for N.

N = 48/8

N = 6

Answer:

A 0.9102

Step-by-step explanation:

A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.

The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.

A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.

A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.

Hence, the correlation coefficient is A, 0.9102

Answer:

B. On the eighth day, the bacteria is 19.90 grams

Step-by-step explanation:

I calculated it logically

Answer:

[tex]t_{n-1,\alpha/2}=3.59114678[/tex]

Therefore we do not have sufficient evidence at [tex]1\%[/tex] level that the true mean diameter has moved away from the target

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=36[/tex]

Mean diameter [tex]\=x=1.4[/tex]

Standard deviation [tex]\sigma=0.5cm[/tex]

Null hypothesis [tex]H_0 \mu=1.5[/tex]

Alternative hypothesis [tex]\mu \neq 1.5[/tex]

Significance level [tex]1\%=0.001[/tex]

Generally the equation for test statistics is mathematically given by

[tex]t=\frac{\=x-\mu}{\frac{s}{\sqrt{n} } }[/tex]

[tex]t=\frac{1.4-1.5}{\frac{0.5}{\sqrt{36} } }[/tex]

[tex]t=-1.2[/tex]

Therefore since this is a two tailed test

[tex]t_{n-1,\alpha/2}[/tex]

 Where

   [tex]n-1=36-1=>35[/tex]

   [tex]\alpha=/2=0.001/2=>0.0005[/tex]

From table

[tex]t_{n-1,\alpha/2}=3.59114678[/tex]

Therefore we do not have sufficient evidence at [tex]1\%[/tex] level that the true mean diameter has moved away from the target

Answer:

A) 32 cm

Step-by-step explanation:

the rectangle could be 12cm x 4cm, giving an area of 48 sq cm

and a perimeter of 24+8 or 32 cm

The given statement can be written as expression given by -

y = 3 ÷ (4 - x)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the statement as -

"3 is divided by the difference of 4 and a number"

Assume the number to be {x}. Then, we can write the expression as -

3 ÷ (4 - x)

Let this expression is equivalent to {y}. We can write -

y = 3 ÷ (4 - x)

Therefore, the given statement can be written as expression given by -

y = 3 ÷ (4 - x)

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Answer:

48,213

Step-by-step explanation:

The full answer is 48,212.5367, but because there is a 5 in the tenths place you round the whole number up

9514 1404 393

Answer:

  49,000

Step-by-step explanation:

The divisor is 4.084. When it is rounded to the nearest whole number, it is 4.

Then the division problem becomes ...

  196,900/4 ≈ 49,000 . . . . . . showing just 2 significant digits for the estimate

__

The point of an estimate is to obtain an approximate answer that is within a few percent of the actual answer. Here, rounding 4.084 to 4.000 gives an error on the order of .084/4 ≈ 2.1%. Because we're using a smaller divisor, the value we obtain for our estimate will be too large by about that amount.

Often, an estimate that has 1 or 2 significant digits is "close enough" for the purpose. Because a change in our estimated value of 1 in the least significant digit is a change of about 2%, we judge this estimate to be "close enough", given the rounding we did to start. Keeping 3 significant digits in our estimate would claim an accuracy that it does not have.

Answer:51x900/100

Step-by-step explanation:

So you’ll do 51 x 900

And then at the denominator when there is no number it is automatically 1 so the denominator will be 100.